A new variability order based on tail-heaviness

Abstract

In this paper, we introduce a new variability order that can be interpreted in terms of tail-heaviness which we will call the tail dispersive order. We provide the new definition, its interpretation and properties and the main characterization. We also study the relationship with other classical variability orders. Finally, we study the tail dispersive order in some classical parametric families and provide some applications in insurance and finance. We conclude with a numerical example applied to log returns distributions.

Keywords:

• dispersive order
• variability orders
• tail-heaviness
• tail risk
• risk measure
• risk capital
• aversion functions
• weighted premiums

Acknowledgements

We are grateful to the anonymous referees and editor for helpful comments which have significatively improved the first version of this paper.

Funding

Miguel A. Sordo and Alfonso Suárez-Llorens acknowledge support received from Ministerio de Ciencia e Innovación (grant number MTM2009-08326) and Consejería de Economía Innovación y Ciencia (grant number P09-SEJ-4739).